The trainer probably isn't the problem unless you try to unlock islands early, but that usually causes problems in LS rather than SF. Which trainer are you using?
The usual cause for no more missions in SF is a full blip pool. A bad cleo mod will keep adding radar blips in the same spot every time the save is loaded until no more markers can be displayed. However, the missions can still be triggered if CJ stands in the correct place. If you start a side-mission like NRG challenge that has lots of radar blips, is there a problem with them being displayed?
If blips are the problem, the site linked below has a Stray Blip tool that might be able to delete some of the extra markers. You'll still need to identify the bad cleo mod to keep the problem from occurring again.
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